3. DISTANCE-TIME THEORY page 2

3.8. The finite speed of space and the inverse speed of time

In the classical and relativity theories, the time axis is defined perpendicular to the three dimensions of space. This space is defined as moving at a finite rate to different points of time on the time axis. Therefore, points of time appear at a finite rate in space. Since the axes of space are defined as perpendicular to the time axis, all points of space occur simultaneously with respect to each other. Hence, the distance between any of these points of space happens at a single point of time and infinitely fast. However, in distance-time theory, distance occurs across a period of time, making distance finitely fast. In other words, each distinct point of a distance happens at a distinct point of time. What this means is that as points of time occur, points of distance occur with them.

As I stated previously, in a distance-time manifold, each observer has a rest speed c across distance-time because the rate of an eventon defining distance-time is speed D/T = c. Also, while these observers are flowing across distance-time at rest speed D/T = c, distance-time is occurring at speed D/T = c between vector coordinates, which happens when measured by an observer with photons in a vacuum. Relative to this observer, therefore, the rate of distance occurring per period of time in any direction is speed D/T = c, and the rate of time occurring across distance is the inverse speed T/D = 1/c. A distance with speed c defined between two objects means that the gap between these objects occurs at a speed c, not infinitely fast. Consequently, consecutive points of distance occur with consecutive points of time in either direction between vector coordinates when a photon travels in either direction between these coordinates.

Points of distance and time can only be defined as occurring when defined as occurring with a particle. Photons in a vacuum are used to measure the speed at which distance occurs because photons in a vacuum move at the same speed as eventons relative to an observer. (Although distance occurs at a finite speed, it still does not occur until measured by an observer through the use of particles. One might wonder what distance at a finite speed is defined between an object and an observer when no particle travels between the observer and an object. I address that question when I discuss the probabilistic location of a particle in chapter 6 of this article.) Since a space is distance defined in three dimensions and since distance has a speed c, I often refer to the speed of space as speed c in distance-time theory. Also, since vector coordinates are defined within a space of finite speed, they also occur at a speed c relative to an observer. This concept of the speed of space having a speed c is in contrast to relativity and classical theories, which defines space as occurring at an infinite speed.

3.9. The finite speed of space versus the expansion of the universe

When I discuss the finite speed of space, some readers may conclude that I am referring to the expansion of the universe. However, this could not be more erroneous! The finite speed of space does not refer to the expansion of space between objects. To further illustrate this, I place a man in a room facing a stationary wall. Relative to this man, the wall is located at a period of time and at a distance away from him. The finite speed of space essentially means that the consecutive points of distance between the man and the wall occur with consecutive points of time as measured by the man through the use of light particles. Therefore, the wall would occur at a distance and a period of time away from the man. This means that the gap between the man and the wall happens at a finite speed because it occurs over a period of time. Obviously, this does not mean that the gap is expanding and the wall is moving away from the man. Instead, it means that the stationary wall would occur with its surrounding space a distance and a period of time away from the man. Since the expansion of the universe actually refers to galaxies moving away from each other, it is obviously a different concept from the finite speed of space. Nevertheless, there may be a connection between the speed of space and the expansion of the universe even though space of speed c is not the same idea as an expanding universe.

3.10. A here-now

Since space has a speed c in distance-time theory, principles requiring a space and time, such as influence at a distance, Heisenberg's uncertainty principle, momentum, and energy, are redefined in a space which occurs at speed c in a distance-time manifold. Consequently, in distance-time theory, the speed of measuring the location or speed of a particle is at a speed c or slower, and any influence across a distance must occur at speed c or slower. On the other hand, in Einstein's relativity theory, the uncertainty principle, influence at a distance, energy, and momentum are defined in a space of infinite speed. Space has this finite speed because time is integrated into it. Any structure of time and space needs to describe space in the future, past, and present. A here-now is space in the present, and it is a point space. A here-now is where at a single point of time there is no difference between locations in space.

Since distance occurs at speed c in a distance-time manifold, at a single point of time, t, only an infinitesimal point of distance occurs between any two distinct vector coordinates. Therefore, at every point of time, distance contracts to zero, an infinitesimal point, between different vector coordinates and results in an infinitesimal space. This means that within a distance-time manifold every vector coordinate at the single point t, the present in time, is located here and now relative to any vector coordinate. Consequently, any particle in a distance-time manifold experiences all other particles in this manifold here and now. I call this infinitesimal space at time now a “here-now”. A here-now contrasts with Einstein's special relativity theory, which assumes that there is an infinitely fast space at the single point of time happening now relative to an observer [1–5]. This point space is infinitely quick because it happens at a single point of time. Also, since a four-dimensional space-time continuum in general relativity theory assumes that space is infinitely fast, a here-now cannot be derived from the theory of general relativity. Therefore, a here-now is an independent concept from the concept of a singularity found in general relativity theory.

Some readers may still be troubled with an entire space that contracts to a single point. I compare the relationship between space and a point of space to an analogy about the relationship of light and darkness. Darkness is essentially the lack of light. Similarly, a point space is the lack of distance within space. Where there is a zero amount of light, there is darkness. When there is zero distance occurring in any direction of space, there is no difference between vector coordinates in space. Thus, all vector coordinates in space define the same location. In other words, a single point of space occurs when zero distance happens at an infinite speed between any vector coordinates.

Distance is only defined within the difference between points of time, but not the here-now, which is only defined at a single point of time. However, both distance-time and the here-now still happen in the same manifold. This seems contradictory. How can both occur in the same manifold? In section 3.6, I illustrated that a here-now at a point of time is distinct because of the distinct set of events it possesses. Therefore, there is a difference between each here-now, which is measurable by the distance-time each eventon traverses between each here-now. Thus, distance can only exist in the difference between points of time, and the here-now can exist only at a single point of time.

One should not think that within a here-now there is zero distance divided by zero time. Instead, within a here-now, there actually exists an infinitesimal point of distance-time. As a consequence, one could only divide an infinitesimal point of distance by an infinitesimal point of time, which would still result in a constant ratio c.

How does one define the concept of zero? It would be easier to define zero in a quantified model of something but not in a continuum of something. In the quantified model of something, that something at its smallest comes in bits. In this type of model, I can simply count the quantity of the bits. If there are no bits, the quantity is zero bits. A continuum is different. What is the concept of zero in a continuum model of something? It is difficult to count the quantity of something that is continuous. When can I count or measure zero of a continuous something? I can say that that continuous something is an infinitesimal. If I use the concept of an infinitesimal, I can state that no matter how small of that continuous something you can measure or count, a zero amount of it is less than that. Distance-time is continuous. A here-now is zero distance-time. The best way to look at a here-now of distance-time is that of an infinitesimal distance-time.

Although the existence of space is communicated to observers by particles with finite speed, it is generally assumed that space exists at a single point of time. One cannot prove, however, that space does exist at a single point of time. To give an example of this, I define a man as standing a distance from a wall. The man wants to prove that there is a gap between him and the wall at the single point of time happening now. In other words, he wishes to prove that space is infinitely quick. The man first bounces a ball off the wall and measures the period of time between the moment the ball leaves and the moment it returns. Although this proves the existence of space between the man and the wall, it does not prove that this space is infinitely quick. The man also realizes that the fastest way he can determine that the wall is a distance away is to measure the distance with a light beam traveling in a vacuum. The difference in time it takes the light to travel between the man and the wall proves that there is a gap occurring between the man and the wall and that this gap occurs at least as fast as the speed of light in a vacuum. However, the man realizes that no object travels faster than the speed of light in a vacuum. Thus, he is unable to prove (measure) that space is infinitely quick. If an observer cannot detect something, that something cannot be defined relative to an observer. In other words, relative to an observer, all that is real is that which is observable. In retrospect, it is erroneous to define an infinitely quick space relative to an observer. Yet, the special theory of relativity does exactly that. In distance-time theory, on the other hand, the gap between the man and the wall does not exist at a single point of time. Therefore, the gap shrinks to zero at a single point of time and the wall is located here-now relative to the man.

To think that all the energy that is in a space is collapsed into a point creating infinite energy would be a wrong view of a here-now. In a here-now, there is zero distance-time and zero frequency-wavelength. As a result, there would also be zero energy in a here-now. Indeed, all principles in physics I discussed earlier, notably Heisenberg's uncertainty principle, influence at a distance, momentum, and energy, seemingly conflict with the here-now because these principles need a space and time in which to be defined. Yet, I reiterate that principles needing a space are not defined as happening at a single point of time. Instead, they are defined across a period of time in a space of speed c. Therefore, they do not conflict with the here-now principle, which is only defined at the single point of time happening in the present relative to an observer. Any structure of time and space needs to describe space in the future, past, and present. A here-now is space in the present, and it is a point space. It is necessary in this article.

3.11. A here-now never overlaps space

A here-now and space only occur relative to an observer. A here-now only happens at the point of time in the present relative to an observer. As a consequence, all other here-nows in the past or future do not exist relative to the observer. On the other hand, relative to an observer, space happens over a period of time into the past or future. In other words, space happens over a period, which is the difference between the present point of time and a point of time in the past or future. Therefore, relative to an observer, space never happens at the single point of time of the present. As a consequence, space and a here-now never occur at the same point of time; nor do they ever overlap relative to an observer. Therefore, any object observed in a space at a point of time, t, in the past could not be located here-now, relative to the observer, at the same point of time, t.

3.12. The effect of two distinct incidents on each other

One question about a point space may trouble some readers. If a space is located at a single point of space at the point of time happening now, how can the force and momentum of a car wreck keep separate from me as I watch television two miles away at the time of the wreck? These two incidents occur at a finite speed and only in a space of finite speed. In general, the laws of physics governing actions and reactions occur in a space of finite speed. (There are possible exceptions to this rule, one of which I discuss in chapter 6 on quantum tunneling.) Since the force and momentum in the car wreck happen in a space of finite speed, they do not occur here-now relative to me. Therefore, the force and momentum in the car wreck happen two miles away and have no effect on my watching television. The solution that I have given to the paradox of the car wreck may be applied to many problems that readers have with the concept of a point space. For instance, how can the human body function in a point space? The answer is that all the reactions within the human body occur within a space of finite speed and not within a point.

A second question may also surface. How can a particle be located within an infinitely fast point space and be measured to have a specific location within a space of finite speed? I best answer this question in section 6.1 of this article, which focuses on the probabilistic location of a particle.

3.13. Measuring a distance between two distinct locations at the same point of time relative to me

Let's for a moment imagine that I am standing in the middle of a room exactly halfway between two opposing walls which I call A and B. I simultaneously emit two photons in opposite directions. One bounces off wall A and returns to me. The other bounces off wall B and returns to me. Since both left me simultaneously, they will both arrive at their respective walls at the same exact time. Hence, I would measure a distance between two walls which coexist at a single point of time, relative to me. How could this result occur, if, at a single point of time, a point space exists? It must be remembered that space is defined relative to an observer and via particles, so the only point space existing relative to me at a given moment is in my now, and not in my future or past. However, relative to me, these two walls coexist at a different point of time from my now and are a distance from me in opposite directions. The only way I could measure a wall in the present time (the now), relative to me, is for me to be at the same point in space as the wall. However, if I were located at either wall, A or B, I could not measure both walls happening at the same point of time and a distance apart from each other. Instead, I would always measure them existing at different points of time and at a distance apart.

3.14. Rod and clock measurements

Traditionally, all measuring rods (rulers) are calibrated to distance units, and all clocks are calibrated to time units. Nevertheless, rods and clocks measure distance-time. Rods measure the distance-time that any object must move across, going straight from one vector coordinate to another. The quantity of distance-time between vector coordinates is defined by the metric function given in Eqs. (1) and (3). Clocks, however, measure the magnitude of distance-time that the entire manifold moves across with its rest velocity. Using the distance-time equation, D = cT, I could divide rod measurements by c to get the time measured by a rod, or I could multiply clock measurements by c to get the scalar distance measurement of clocks. However, rod and clock measurements are not necessarily equated because they can measure independently from each other. Consequently, a rod measurement divided by a clock measurement can equal any speed, though not necessarily speed c. The distance-time equation only states that distance is equivalent to time, and not that a rod measurement is equal to a clock measurement. However, the magnitude of a rod measurement is equal to a clock measurement when a rod and clock measure the distance-time traversed by the same photon traveling at speed c.

3.15. The speed of rod measurements

In Einstein's relativity theory, the rod measurement was assumed to be infinitely quick because space was defined as infinitely fast [1–5]. Nevertheless, no object travels faster than the speed of light in a vacuum; therefore, I have no object by which to measure the speed of the rod measurement at speeds faster than that of light in a vacuum. Despite these circumstances, I could measure the minimum possible speed at which the rod measurement occurs. Placing a rod in a vacuum, I could measure the difference in time that a photon travels from one end of the rod to the other. This measurement would determine that speed c is the minimum possible speed, though not necessarily the actual speed, and that one end of the rod occurs a distance away relative to the other end. Nevertheless, I could merely validate the minimum possible speed of the rod measurement, and the relativistic view of an infinitely quick rod measurement would remain only an assumption.

In contrast to this relativistic view, the determinable minimum possible speed c of the rod measurement is the speed of the rod measurement in distance-time theory because that is the speed of distance in distance-time theory. I send a photon on a straight path along a rod measurement. The path, direction, and speed of the photon and the distance-time traversed by it between the rod ends are the rod measurements. As a result, the rod end that it encounters first occurs first, and the rod end that it encounters last occurs last.

To further illustrate these concepts, I create a thought experiment. In my imagination, I send a photon along a rod in a vacuum, and I place an observer at both ends of the rod. Relative to the observer at the rod end that encounters the photon last, the other rod end occurs at a negative distance-time away. Relative to the observer at the rod end that encounters the photon first, the other rod end occurs at a positive distance-time away. Since a different photon could be traveling the same path but in an opposite direction, the order of which rod end occurs first or last would depend on which photon is being observed.